407881: GYM102916 E Powerless Mage

A mage knows n spells, the i-th of which requires q_i blue mana, w_i purple mana and e_i orange mana (q_i + w_i + e_i > 0). Let's say the mage has Q blue mana, W purple mana and E orange mana, and denote the total amount of mana Q + W + E as R. Knowing that the mage is unable to cast any spell, what can be the maximal value of R?

The first line contains an integer n (1 ≤ n ≤ 200000) — the number of spells.

Each of the next n lines contains three integers q_i, w_i, e_i (0 ≤ q_i, w_i, e_i ≤ 10⁹, q_i + w_i + e_i > 0) — the manacosts of the i-th spell.

Output the maximal total amount of mana R such that the mage is unable to cast any spell.

If this number is infinitely large (for any total amount of mana R, there could be a situation so that the mage is unable to cast any spell), output "Infinity".

4
0 0 100
0 100 0
100 0 0
61 71 81

278

6
0 0 100
0 100 0
100 0 0
0 11 61
11 61 0
61 0 11

180

3
3 1 1
1 3 1
1 1 3

Infinity